A three-way three-mode extension of De Boeck and Rosenberg's (1988) two-way
two-mode hierarchical classes model is presented for the analysis of indiv
idual differences in binary object x attribute arrays. In line with the two
-way hierarchical classes model, the three-way extension represents both th
e association relation among the three modes and the set-theoretical relati
ons among the elements of each mode. An algorithm for fitting the model is
presented and evaluated in a simulation study. The model is illustrated wit
h data on psychiatric diagnosis. Finally, the relation between the model an
d extant models for three-way data is discussed.